Optimisation of planing

Table of Contents

1. Introduction

This document contains a description of optimisation tools for electric system planing simulation. If you are only interested in operation you might prefer to go back to file optim-Operation.ipynb. In files BasicFunctionalities/input-XXX.ipynb you can learn to understand input data (consumption, availability).

(Text below is almost the same as for operation)

This document will gives a chance to understand

It proposes to enter the subject by increasing progressively the number of variables and constraints in the optimisation problem, hence moving toward more realism through the document, introducing:

It relies on different test cases that allow to

If, after reading this file, you want to build your own pyomo model you can go to optim-Planing-Advanced.ipynb.

2. First basic problem

2.1. Math and first step with pyomo for solving problem

Before you start with the math, you should

\begin{align} &\text{Cost function }& &\min_{x,\bar{x}} \sum_i \left ( \beta_i\bar{x_i}+ \sum_t\pi_i x_{it}\right ) \;\;\; & & \pi_i \text{ marginal cost, }\beta_i \text{fixed annualized cost}\\ &\text{Power limit } & &\text{ s.t.} \;\; 0 \leq x_{it}\leq a_{it} \bar{x_i} & &\bar{x_i} \text{ installed power, } a_{it} \text{ availability}\\ &\text{Meet demand } & & \sum_i x_{it} \geq C_t && C_t \text{ Consumption}\\ \end{align}

2.2 Analysing results : lagrange multipliers

Verify that the sum of market prices allows all actors to cover fixed and marginal cost. do they earn more ? why ?

3. Extensions of this operation problem

3.1. Linear temporal coupling with ramp constraints

In the this section, we will increase the complexity of the problem given in Section 2 and add : dependency on area z (country), a congestion constraint, ramp constraints.

\begin{align} &\text{Cost function }& &\min_{x} \sum_z \left ( \beta_{iz}\bar{x_{iz}}+ \sum_t \sum_i \pi_{iz} x_{itz}\;\;\; & & \pi_{iz}\right ) \text{ marginal cost}\\ &\text{Power limit } & &\text{ s.t.} \;\; 0 \leq x_{itz}\leq a_{itz} \bar{x_{iz}} & &\bar{x_{iz}} \text{ installed power, } a_{itz} \text{ availability}\\ &\text{Meet demand } & & \sum_i x_{itz} \geq C_{tz} && C_{tz} \text{ Consumption}\\ &\text{Stock limit } & &\sum_t x_{it}\leq E_i && E_i=\bar{x_i}*N_i \text{ Energy capacity limit}\\ &\text{ramp limit } & &rc^-_i *x_{it}\leq x_{it}-x_{i(t+1)}\leq rc^+_i *x_{it} && rc^+_i rc^-_i\text{ ramp limit}\\ \end{align}

3.2. Linear spatio-temporal coupling with ramp+spatial constraints

Math here are in 3.1

4. Storage operation

4.1. Optimisation of a storage market participation

Just have a look at optim-Storage.ipynb

4.2. Simultaneous optimisation of storage and electric system

This section is a bit more difficult that the other one. You can skip the math if you're only interested in using the storage optimisation tool.

Case V is in section 5. (lots of renewable)

4.3. Simultaneous optimisation of storage+spatial and electric system

5. System with a lot of renewable

TODO here : add electrolysers